SlowGuess/NeurIPS_2023_OCR huggingface dataset:
In addition, maintaining the same training recipes except setting the number of epochs as 50, we trained the models using OC20 dataset [29]; the training results are visualized in Figure C.3 (c). Training recipes of OC20 benchmark are different from ours. For instance, the target energy values of snapshots are adjusted by subtracting so-called reference energy, which corresponds to the energy of an initial snapshot with the same trajectory as the snapshots, and then apply the normalization technique for the shifted energy values; in contrast, we use the target energy values and apply peratom energy normalization. Furthermore, DimeNet++ and GemNet-dT used for OC20 benchmark
(b) HfO
(c) OC20
Figure C.3: EF metrics of 10 MLFF models trained with MSE- and MAE-based loss functions.
have larger architectures than those introduced in their original papers, while we utilize the original architectures; nevertheless, they show prominent results in energy and force prediction.
Overall, GNN-based models experience high-ranked performance. GNNs incorporating equivariance, such as Allegro and MACE, demonstrate inferior performance in energy and force prediction compared to SchNet, which is already considered the least favorable model in SiN and HfO datasets. For models except BPNN and Allegro, differences between the training results of two loss functions are less than those in SiN and HfO datasets, and EF metrics of using MAE-based loss are very slightly higher than using MSE-based loss. The results obtained from BPNN, where EF metrics of the model trained with MAE-based loss on both val_id and val_oodboth are higher, imply that descriptor-based models may experience a significant performance drop, when dealing with datasets containing a wide range of atom species such as OC20. Allegro trained with MAE-based loss may be reasonably trained when observing the results of val_id, but fails to correctly predict energy and forces on OOD data of OC20, referred to as val_oodboth. It may be beneficial to analyze which factors of Allegro bring about such failure, because Allegro is compatible with the parallel computing of MD simulation tools such as LAMMPS while the other models cannot, which is important to enable large-scale simulations using MLFF models.
C.4.2 Results of Model Exploration Study
The numerical results of model exploration study, which are discussed in Section 4.3 and visualized in Figure 3, are listed in Table C.4, where the variation scales of each model and corresponding model sizes (i.e., the number of parameters) are also included. The result of DPA-1 shows that DPA-1 can locate on the pareto-frontier in Figure 3. DPA-1, among the models evaluated in this study, is the only model that can be operated exclusively in DeePMD-kit [48], a TensorFlow-based framework. Therefore, the result of DPA-1 was excluded from Figure 1 because it may not be appropriate to directly compare that with the results of other models obtained from our PyTorch-based framework.
C.5 Data Scaling Effect
We additionally present the data scaling effect, which may be helpful to make a training strategy for MLFF researchers. We follow the experimental settings of previous works [22, 24], where the
Table C.3: Numerical results (EF metrics) of MLFF models, visualized in Figures 1 and C.3.
Model	Loss	Train	SiN Test	OOD	Train	HfO Test	OOD	train	OC20 val_id	val_oodboth
BPNN	MSE-based	393.3	466.2	566.0	219.2	220.5	232.7	477.2	495.0	701.1
MAE-based	291.4	316.2	459.4	206.4	210.2	227.4	984.2	991.3	991.5
DPA-1	MSE-based	335.0	347.1	472.0	232.7	234.0	257.1	127.8	128.9	184.6
MAE-based	309.9	325.5	471.2	246.2	247.0	274.3	131.1	132.9	190.0
SchNet	MSE-based	192.0	471.2	820.7	171.5	417.4	506.4	145.3	147.2	219.8
MAE-based	114.6	453.5	849.1	190.8	408.3	500.6	152.1	153.1	238.2
DimeNet++	MSE-based	84.3	119.8	188.3	37.1	48.0	69.7	102.1	88.2	131.9
MAE-based	64.8	124.1	213.3	42.8	51.6	76.9	108.8	93.0	141.1
GemNet-T	MSE-based	144.5	164.9	184.9	43.0	45.8	62.7	113.4	102.4	130.9
MAE-based	98.2	118.1	142.7	27.3	33.0	54.3	112.1	102.0	130.1
GemNet-dT	MSE-based	138.5	158.5	201.0	53.4	56.8	75.2	110.3	98.3	130.7
MAE-based	87.9	120.4	171.1	36.3	41.9	67.2	103.4	91.4	124.5
NequIP	MSE-based	163.0	174.4	245.5	75.1	79.6	104.5	133.9	126.3	180.4
MAE-based	157.9	170.4	245.1	79.8	82.6	117.8	140.7	135.0	200.4
Allegro	MSE-based	236.2	245.1	344.6	152.5	156.2	227.4	168.9	163.7	213.7
MAE-based	209.0	225.4	349.3	152.7	156.0	360.5	169.4	169.6	2.1e+14
MACE	MSE-based	186.7	190.3	252.0	62.8	64.6	136.3	153.2	146.8	411.8
MAE-based	147.1	155.1	217.7	65.7	66.2	92.2	164.5	158.5	218.4
SCN	MSE-based	138.2	153.5	230.0	50.4	56.9	81.1	-	-	-
MAE-based	50.2	97.9	170.0	30.1	41.5	67.3	105.5	87.7	135.6
ReduceLROnPlateu scheduler is used to train MLFF models. Even though the training steps cannot be fixed due to this scheduler unlike our setting, we anticipate that their training might be stopped at similar update steps. Thus, in this data scaling experiments, MLFF models are trained by the fixed number of steps for model update; the setting is referred to as the equal budget setting. We randomly sample  $20\%$ ,  $40\%$ ,  $60\%$ , and  $80\%$  snapshots from the HfO training set (i.e., 5.6k, 11.2k, 16.8k, and 22.4k), and trained models by 1000, 500, 334, and 250 epochs, correspondingly, according to the equal budget setting. We select six models (BPNN, GemNet-T, GemNet-dT, NequIP, Allegro, and MACE) and obtain their energy and force errors using the HfO test and OOD sets. Except the data size and epochs, the training recipe used in the MAE-based training experiments of Figure 1 is maintained.
The results are reported in Table C.5 and visualized in Figure 4. For all models, as more training data are used, the training error increases while both the test error decreases, where the gap between these two errors also decrease. The OOD error decreases in most cases. Therefore, our data scaling results suggest that training with fewer epochs and more data can be helpful to improve the generalization performance of MLFF models. Meanwhile, the difference between EF metrics using  $80\%$  and  $100\%$  of training set is marginal, meaning that the performance improvement that can be gained by using more data seems to be saturated. Such observation implies that our training set sampled from the raw dataset is sufficient for our semiconductor MLFF benchmark.
We can opt for another data scaling experimental setup where the identical training epochs are used to train MLFF models; the setting is referred to as the equal epoch setting. In the equal epoch setting, as the training set size is reduced, the number of model update steps is also reduced. Considering that accuracy drop was clearly observed when using less data at the equal budget setting, we omit the experiments of the equal epoch setting because further accuracy drop is intuitively expected.
D Details of Properties Benchmark
D.1 Radial and Angular Distribution Functions
The dynamic indicators, namely RDF and ADF, are classified as such since they are derived from high-temperature MD simulation trajectories. In order to investigate the stability of models in different atomic environments induced by high turbulence or active movement caused by high thermal energy,
Table C.4: Numerical results visualized in Figure 3 (HfO test set). Double, Base, Half, and Quarter indicate the range of the relative variation scale  $\{2\mathrm{x},1\mathrm{x},0.5\mathrm{x},0.25\mathrm{x}\}$ , correspondingly.  $^{\dagger}$ DPA-1 is specifically designed for use with DeePMD-kit, whereas the other models are implemented and evaluated within our framework.
Model	Variation scale	Number of Params.	EF metric	Inference time (ms)
BPNN	Double	1.92M	356.9	31.2
Base	0.50M	356.1	31.5
Half	0.13M	358.9	32.1
DPA-1†	Base	6.14M	234.0	23.9
SchNet	Double	35.61M	743.6	24.3
Base	9.09M	687.8	23.4
Half	2.37M	627.0	23.1
Quarter	0.64M	692.3	24.8
DimeNet++	Base	1.89M	81.8	62.5
Half	0.48M	111.6	68.3
Quarter	0.13M	145.2	68.9
GemNet-T	Base	1.89M	51.1	64.3
Half	0.48M	67.6	62.1
Quarter	0.13M	94.5	62.4
GemNet-dT	Double	9.14M	55.0	34.5
Base	2.31M	64.7	29.5
Half	0.59M	84.7	24.9
NequIP	Double	1.45M	113.9	62.1
Base	0.36M	133.4	62.0
Half	0.09M	160.0	61.3
Quarter	0.02M	197.5	57.0
Allegro	Double	5.61M	243.1	48.7
Base	1.40M	263.1	30.0
Half	0.35M	289.9	27.4
MACE	Double	0.26M	86.1	35.6
Base	0.11M	104.3	36.2
Half	0.05M	128.3	35.9
SCN	Base	1.58M	62.2	327.2
Half	0.47M	90.9	316.2
Quarter	0.13M	183.3	332.2
we carefully selected high temperatures for SiN (1200 K) and HfO (1200 and 1800 K). RDF, also known as the pair correlation function, captures the changes in density relative to the distance from a chosen reference particle. On the other hand, ADF expands the scope of analysis beyond radial distances and centers on characterizing the angular distribution of particles surrounding a reference particle. The analysis of RDF and ADF plays a fundamental role in simulations as it enables the identification of structures, phases, and interactions. Moreover, it provides a deeper understanding of behaviors and reactions occurring within solids.
The radial distribution function,  $g(r)$  is an average density of particles within distance  $r$ , which is represented by
$$
g (r) = \frac {\mathrm {d} n _ {r}}{4 \pi \rho r ^ {2} \mathrm {d} r}, \tag {4}
$$
where  $\rho$  indicates an average density of the system.
For compound AB, there could be three types of RDF results: A-A, A-B, and B-B. Mean Absolute Error (MAE) was calculated against the DFT reference for each case. The resulting three MAE values were then averaged to obtain the RDF error for each specific structure. Similarly, ADF could yield six types of results: A-A-A, B-B-B, A-B-A, B-A-B, A-A-B, and B-B-A. For each ADF case, the
Table C.5: Numerical results visualized in Figure 4.
Model	Training set size (ratio)	EF Metric (↓)	Model	Training set size (ratio)	EF Metric (↓)
Train	Test	OOD	Train	Test	OOD
BPNN	5.6k (20%)	190.1	231.4	260.6	NequIP	5.6k (20%)	72.5	99.4	174.6
11.2k (40%)	200.9	216.4	239.1	11.2k (40%)	76.6	88.1	148.5
16.8k (60%)	204.1	212.9	232.4	16.8k (60%)	78.1	84.2	130.0
22.4k (80%)	205.8	210.8	230.8	22.4k (80%)	79.0	82.5	119.1
28.0k (100%)	206.4	210.2	227.4	28.0k (100%)	79.8	82.6	117.8
GemNet-T	5.6k (20%)	19.8	48.9	75.2	Allegro	5.6k (20%)	144.7	174.6	1923.8
11.2k (40%)	23.6	39.3	64.7	11.2k (40%)	148.9	163.8	658.3
16.8k (60%)	25.1	35.2	59.2	16.8k (60%)	150.8	157.5	365.8
22.4k (80%)	26.0	33.3	54.1	22.4k (80%)	152.0	156.4	415.3
28.0k (100%)	27.3	33.0	54.3	28.0k (100%)	152.7	156.0	360.5
GemNet-dT	5.6k (20%)	25.1	62.4	91.8	MACE	5.6k (20%)	61.7	71.0	221.6
11.2k (40%)	31.7	49.0	79.2	11.2k (40%)	64.3	68.3	180.4
16.8k (60%)	34.4	44.4	73.0	16.8k (60%)	65.1	67.6	126.0
22.4k (80%)	35.3	42.1	67.0	22.4k (80%)	66.4	67.3	114.6
28.0k (100%)	36.3	41.9	67.2	28.0k (100%)	66.1	66.3	92.2
MAE was calculated by comparing it to the respective DFT reference. The resulting six MAE values were then averaged to obtain the ADF error for each specific structure.
To compare two distribution functions, we employ L1 distance between distribution functions. Thus an error metric of a RDF  $g(r)$  generated by a MLFF is defined by
$$
E _ {\mathrm {R D F}} = d (g, g _ {\mathrm {D F T}}) = \frac {1}{R _ {c}} \int_ {0} ^ {R _ {c}} | g (r) - g _ {\mathrm {D F T}} (r) | \mathrm {d} r \tag {5}
$$
where,  $R_{c}$  is equal to  $6\mathring{\mathrm{A}}$
Similarly, an error of an ADF  $h(\theta)$  is defined by
$$
E _ {\mathrm {A D F}} = d (h, h _ {\mathrm {D F T}}) = \frac {1}{\pi} \int_ {0} ^ {\pi} | h (\theta) - h _ {\mathrm {D F T}} (\theta) | \mathrm {d} \theta . \tag {6}
$$
In both datasets, high-temperature simulations with various initial structures were conducted for a duration of 6 ps. Ground truth trajectories were computed using DFT. RDF and ADF were computed by averaging the last 3 ps of the simulation; a total of 50 snapshots were averaged, with an interval of 6 fs between each snapshot. The simulated structures employed in this study were supercells, encompassing a varying number of atoms. Specifically, the supercells comprised a range of 2,592 to 3,456 atoms for HfO and 1,296 to 2,835 atoms for SiN (refer to Table D.1 for additional information). This range of atom counts facilitates future scalability studies of MLFF. Additionally, users have the flexibility to increase supercell sizes as desired.
For the SiN, four different structures were simulated at  $1200\mathrm{K}$ . Two structures with Si:N ratios of 3:4 and 1:1, which were within the range of ratios covered by the training dataset, were used to compute  $\mathrm{RDF^{ID}}$  and  $\mathrm{ADF^{ID}}$ . The  $\mathrm{RDF^{ID}}$  value was calculated by averaging the RDF errors of the two structures, and likewise, the  $\mathrm{ADF^{ID}}$  value was obtained by averaging the ADF errors of the two structures. Additionally, two structures with Si:N ratios of 1:2 and 3:2, which were outside the range of ratios present in the training dataset, were employed to calculate  $\mathrm{RDF^{OOD}}$  and  $\mathrm{ADF^{OOD}}$ .
A total of eight structures were simulated for the HfO. Among these, five structures were simulated at 1200 and  $1800\mathrm{K}$  (resulting in a total of 10 simulations) using the same stoichiometry  $(\mathrm{Hf}:\mathrm{O} = 1:2)$  as in the training set. These simulation trajectories were then used to calculate  $\mathrm{RDF^{ID}}$  and  $\mathrm{ADF^{ID}}$ . On the other hand, the remaining three structures were considered out-of-distribution structures with varying stoichiometries of Hf:O, specifically 1:1, 2:3, and 4:7. These three structures were simulated at  $1200\mathrm{K}$  and then employed to calculate  $\mathrm{RDF^{OOD}}$  and  $\mathrm{ADF^{OOD}}$ .
D.1.1 Understanding RDF & ADF: Insight, Motive, and Explanation
In simulation studies, understanding atomic position patterns can be complex. To solve this, researchers turn to RDF and ADF, two pivotal post-processing techniques, to differentiate between
Table D.1: Details of evaluated structures for RDF and ADF. Structures with index (idx.) indicate the same crystal family but have different lattice constants. The index numbering has been restarted for each dataset (e.g., Cubic (1) of SiN and Cubic (1) of HfO have different lattice constants).
Data	Distribution	Structure (idx.)	Hf:O (or Si:N)	# atoms (3×3×3)	Temp.
SiN	ID	Amorphous	1:1	1296	1200 K
Triclinic	3:4	2835	1200 K
OOD	Cubic (1)	1:2	2592	1200 K
Cubic (2)	3:2	2720	1200 K
HfO	ID	Monoclinic	1:2	2592	1200 & 1800 K
Tetragonal	1:2	2592	1200 & 1800 K
Cubic (1)	1:2	2592	1200 & 1800 K
Orthorhombic (1)	1:2	2592	1200 & 1800 K
Orthorhombic (2)	1:2	2592	1200 & 1800 K
OOD	Hexagonal (1)	1:1	3456	1200 K
Hexagonal (2)	2:3	3240	1200 K
Cubic (2)	4:7	2376	1200 K
Figure D.1: RDFs of  $\alpha\text{-Si}_3\mathrm{N}_4$  (left) and liquid-  $\mathrm{Si}_3\mathrm{N}_4$  (right).
materials or states. RDF quantifies atomic or molecular density fluctuations based on distance, providing insights into localized structural properties. In contrast, ADF elucidates angular tendencies between particle triplets, offering a perspective on molecular shapes and bonding angles. Collectively, they act as benchmarks, verifying the real-world alignment of simulations.
At the heart of MLFF models lies the ability to accurately predict energies and forces governing atoms and molecules. These predictions are crucial as they directly influence the movement, behavior, and interactions of atoms, which, in turn, dictate the patterns seen in RDF and ADF. When the RDF and ADF predicted by an MLFF closely align with those from DFT calculations, it's a strong indication that the model is capturing the essential physics and is making accurate energy and force predictions.
RDF and ADF can be used to capture phenomena such as phase transitions, system characteristics, and intermolecular dynamics. A prime example is the simulation of the silicon nitride phase shift from solid to liquid, where stark RDF modifications are observable in Figure D.1. What begins as distinct peaks in its crystalline form smoothes out during the melting process, signifying inherent structural shifts. Figure D.1 contrasts the RDF patterns of crystalline silicon during its initial state and postmelting phase, underlining the transformative effects of atomic rearrangements. Such configurations inherently relate to the balance of interatomic forces and the resultant energy landscape. When atoms approach each other under specific conditions, they might form bonds due to attraction or repel, settling into stable distances. This equilibrium gives rise to distinctive RDF and ADF profiles that mirror these atomic positions.
While RDF and ADF primarily help visualize atomic configurations, they also play a crucial role in assessing the fidelity of atomic paths predicted by MLFF. For example, in Figure D.3-(c), there is a noticeable anomaly in the RDF for Hf-Hf interactions on the OOD Hexagonal (2) structure when obtained using the MAE-based SchNet model. This anomaly is characterized by a pronounced peak at unusually short 'r' distances. This unlikely closeness between Hf-Hf atoms, especially when
(a) MAE-trained models on ID Amorphous Cubic (2), 1200K, (Si-N)
(c) MAE-trained models on OOD Cubic 2
Figure D.2: RDF comparisons: DFT ground truth vs. model predictions for SiN in ID Amorphous and OOD Cubic 2 structures.
(b) MSE-trained models on ID Amorphous Cubic (2), 1200K, (Si-N)
(d) MSE-trained models on OOD Cubic 2
compared to ground truth data, not only challenges physical rationale but also signals potential weaknesses in the predictive capability of the MLFF model.
In our framework, we introduce straightforward evaluations of RDF and ADF for MLFF models by contrasting them against reference profiles from gold-standard DFT simulations (Table D.1). A close match between the MLFF-derived profiles and these references signifies model accuracy. Though a smaller error naturally indicates superior model performance, for visualization in the form of radar plots as shown in Figures D.13 and D.14, we inversely transform the RDF and ADF errors such that a value of 1 denotes optimal performance. The specifics of this transformation are detailed in Section D.4.
D.2 Bulk Modulus and Equilibrium Volume
The bulk modulus and equilibrium volume derived from the Birch-Murnaghan equation of state (EoS) are critical in investigating thin film materials, including silicon nitride andd hafnium oxide. The bulk modulus provides insights into the mechanical stability of these films, indicating their resistance to volume shifts under varying pressure conditions and their resilience against external stresses. Additionally, it characterizes the elastic properties of the films, impacting aspects like flexibility and hardness. Meanwhile, the equilibrium volume aids in understanding the relationship between the film's thickness and residual stress, enabling us to evaluate the film's state (strained or relaxed), and refine the growth procedure. Furthermore, both these parameters influence the interfacial properties such as adhesion strength and interface energy, integral for the performance and stability of thin film systems. Comprehension of these parameters is essential for engineering thin films with the required properties, for their potential application in electronics, optoelectronics, and microelectromechanical systems.
The bulk modulus is a fundamental quantity that measures a material's resistance to compression and expansion. It quantifies the material's ability to withstand changes in volume when subjected to external pressure. Comparing the bulk moduli of different materials allows for the assessment of their relative compressibility and overall mechanical strength. Additionally, the equilibrium volume, obtained through the fitting of the Birch-Murnaghan EoS, represents the volume at which the material
(a) MAE-trained models on ID Orthorhombic 2 Hexagonal (2),1200K,Hf-Hf
(c) MAE-trained models on OOD Hexagonal 2
Figure D.3: RDF comparisons: DFT ground truth vs. model predictions for HfO in ID Orthorhombic 2 and OOD Hexagonal 2 structures.
(b) MSE-trained models on ID Orthorhombic 2 Hexagonal (2),1200K,Hf-Hf
(d) MSE-trained models on OOD Hexagonal 2
possesses the minimum energy. Determining the equilibrium volume enables the identification of the most energetically stable configuration of the material, providing insights into its structural stability and phase transitions.
The bulk modulus and equilibrium volume can be obtained by fitting the Birch-Murnaghan EoS. The EoS establishes a relationship between the energy and volume of a solid material, and it can be expressed as follows:
$$
E (V) = E _ {0} + \frac {9 \mathbf {V} _ {0} \mathbf {B} _ {0}}{1 6} \left\{\left[ \left(\frac {\mathbf {V} _ {0}}{\mathbf {V}}\right) ^ {2 / 3} - 1 \right] ^ {3} \mathbf {B} _ {0} ^ {\prime} + \left[ \left(\frac {\mathbf {V} _ {0}}{\mathbf {V}}\right) ^ {2 / 3} - 1 \right] ^ {2} \left[ 6 - 4 \left(\frac {\mathbf {V} _ {0}}{\mathbf {V}}\right) ^ {2 / 3} \right] \right\}, \tag {7}
$$
where  $\mathrm{V}_0$  is the equilibrium volume,  $\mathrm{B}_0$  is the bulk modulus, and  $\mathrm{B}_0^{\prime}$  is the derivative of the modulus with respect to pressure.
The internal energy versus volume data obtained from DFT calculations served as reference to assess the accuracy of MLFF models. In the case of HfO, five crystalline structures present in the training set were utilized to calculate  $\mathbf{B}_0^{\mathrm{ID}}$  and  $\mathbf{V}_0^{\mathrm{ID}}$ . Additionally, one crystal with different stoichiometry, not included in the training set, was employed to determine  $\mathbf{B}_0^{\mathrm{OOD}}$  and  $\mathbf{V}_0^{\mathrm{OOD}}$ . Similarly, in the case of SiN, five different crystalline structures with varying numbers of atoms were used in the EoS evaluation. Among these structures, three were included in the training set and employed to calculate  $\mathbf{B}_0^{\mathrm{ID}}$  and  $\mathbf{V}_0^{\mathrm{ID}}$ . The remaining two structures, which was not commonly found in the training set, was utilized to determine  $\mathbf{B}_0^{\mathrm{OOD}}$  and  $\mathbf{V}_0^{\mathrm{OOD}}$ . For more detailed information regarding the structures evaluated please refer to Table D.2. The values of  $\mathbf{B}_0^{\mathrm{ID}}$ ,  $\mathbf{B}_0^{\mathrm{OOD}}$ ,  $\mathbf{V}_0^{\mathrm{ID}}$ , and  $\mathbf{V}_0^{\mathrm{OOD}}$  were determined by calculating the arithmetic mean of the absolute percentage errors for the evaluated structures.
D.2.1 Understanding the Equation of State: Insight, Motive, and Explanation
Our paper introduces the equation of state as an evaluation method, with metrics derived from the EoS, specifically the bulk modulus  $(\mathrm{B_0})$  and equilibrium volume  $(\mathrm{V_0})$ , serving as the primary assessment metrics. These metrics offer a way to assess how closely the predictions of the MLFF models align with the results from more established methods, like DFT.
Table D.2: Details of evaluated structures for EoS.
Distribution	Space Group	Hf-O (or Si-N) ratio	Number of atoms
SiN	ID	P31c	3:4	28
P1	3:4	14
P1	3:4	28
OOD	Fd3m	3:4	14
Fd3m	3:4	56
HfO	ID	P21/c	1:2	96
P42/nmc	1:2	96
Fm3m	1:2	96
Pbca	1:2	96
Pnma	1:2	96
OOD	Fd3m	4:7	88
The bulk modulus provides insights into a material's resistance to compression. In simple terms, it helps us understand how much a material can be compressed. A higher value indicates that the material is less likely to change its volume under pressure. The equilibrium volume, on the other hand, tells us about the optimal volume where a material is most stable and uses energy most efficiently.
The core requirement of the MLFF model is its capability to simulate atomic interactions. When these interactions are observed at a larger scale, they manifest as properties such as the material's resistance to compression and its most stable form. These properties are effectively represented by metrics like the bulk modulus and equilibrium volume. This suggests that a model which can accurately predict atomic interactions is also likely to be proficient at predicting these larger-scale properties.